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- Question 1 function given by Suppose that X and Y have a joint probability density ce-3r-5y if x, y 20 fx.x(x, y) = %3D otherwise Dete the value of the normalization constant c. (b Find the marginal probability density function fx and state the name of the distribution of X. (YFind the conditional probability density function fyjx=z- (Y Are the random variables X and Y statistically independent? Justify your answer. Consider now a different joint probability density function for X and Y, namely fxx(x, y) = J12ye-3z-2y if r, y 20 otherwise OWhat is the probability P(Y2 > 2X > 0) ?Book name Mathematical statistics by John Fred 8th edition Chp 3 Question 7852 l l 0.5 If P(A/B)=0.5 and P(B)=0.8, then the 1/1 probability that both A and B occur is O 0.8 O 0.2 O 0.6 0.4 If f(x)=(2x+3)/1O, where 0A Moving to the next question prevents changes to this answer. tion 9 Elongation (in %) of steel plates treated with aluminum is a random variable with the probability density function for 18 < x < 24 f(x) = {126 otherwise Find the variance of the elongation. O 2.980 O 8.222 5.297 O 3.190 A Moving to the next question prevents changes to this answer. MacBooQI. The probability mass function of a random variable X is given by p(i) = ca' /i!, i = 0,1,2,..., where à is some positive value. Find (a) P{X = 0} and (b) P{X > 2}. %3DQUESTION 3 The thickness (in mm) of a steel wire is a random variable with the following probability density function fo-0.75 x2 (2x) for 0need help with this thanksMany random number generators allow users to specify the range of the random numbers to be produced. Suppose you specify that the random number Y can take any value between 0 and 6. Then the density curve of the outcomes has constant height between 0 and 6 and height O elsewhere.Probability and stats1. The loss due to a fire in a commercial building is modelled by a random variable X with density function Let X be a random variable with probability distribution table given below 10 20 50 100 P(X=x) | 0.4 | 0.3 | 0.15 | 0.1 | 0.05 Prepare the cdf of X.Below is the life table of a population of waterbuck. What is the probability that an individual in stage 2 will survive to stage 3 (give your answer to three decimal places)? Stage 0 1 2 3 4 5 ax 50 39 25 20 11 4 Answer: 0.200 1.00 0.78 0.50 0.40 0.22 0.08 Ix dx 11 14 5 9 7 4 Probability of survival = lx+1/lx The correct answer is: 0.8 0.220 0.359 0.200 0.450 0.636 1.000 qx XQuestion 2 The probability density function of the reliability of a piece of equipment is given by: a x)= a(162 – x²³) (x)=(a/1 16-x³ 0SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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